Rewrite as a simplified fraction. ${1.1\overline{64} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1164.6464...\\ 10x &= 11.6464...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1153}$ ${x = \dfrac{1153}{990}} \text{or} {1 \dfrac{163}{990}}$